The Prince displays us a darker side in the second installment of this game
One thing that many players will notice is the jurastic change in the Prince's attitude. He is no longer the kind sounding Prince of the first game, but sounds like a hardened warrior, very mean and uncaring. Some did not like this new Prince and I can hardly blame them.
This game is very similar to the Sands of time, in that the environment is still one big puzzle, one change is that you switch between a past and present time period bu using time gates located around the island. These are needed as some places and events are only accessible in either the past or the present.
Another change is in the fighting style. The Prince no longer uses the Dagger of Time as his secondary weapon, but instead can pick up enemies weapons, or keep his hand free, allowing for him to throw enemies and other such moves. The fighting is more free form, allowing you to custimize a fighting style that is just right for you.
The Prince still has control over the Sands of Time, and they are still very important to your success. The Prince may rewind time, if you do something you wished not to do, you may rewind time a short distance so that you never did it, and he can still slow time down, allowing access to doors that you couldn't get through otherwise due to the fact that they are too far away, or close too fast or other such things.
One other thing I will mention is that this game has an alternate ending. If you aquire all 9 health upgrades before the end of the game, you will see an alternate ending that will make Prince of Persia: The Two Thrones make more sense, because they based the third game off of Warrior Withins alternate ending.